TSTP Solution File: NUM020^1 by E---3.1.00

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM020^1 : TPTP v8.1.2. Released v3.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat May  4 08:47:30 EDT 2024

% Result   : Theorem 0.22s 0.52s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   31 (  25 unt;   6 typ;   0 def)
%            Number of atoms       :   25 (  24 equ;   0 cnn)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :  129 (   5   ~;   0   |;   0   &; 124   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   89 (  89   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   6 usr;   1 con; 0-4 aty)
%            Number of variables   :   50 (  10   ^  38   !;   2   ?;  50   :)

% Comments : 
%------------------------------------------------------------------------------
thf(decl_24,type,
    two: ( $i > $i ) > $i > $i ).

thf(decl_25,type,
    three: ( $i > $i ) > $i > $i ).

thf(decl_28,type,
    six: ( $i > $i ) > $i > $i ).

thf(decl_35,type,
    mult: ( ( $i > $i ) > $i > $i ) > ( ( $i > $i ) > $i > $i ) > ( $i > $i ) > $i > $i ).

thf(decl_36,type,
    esk1_2: ( ( $i > $i ) > $i > $i ) > $i > $i ).

thf(decl_37,type,
    esk2_1: ( ( $i > $i ) > $i > $i ) > $i ).

thf(thm,conjecture,
    ? [X3: ( $i > $i ) > $i > $i] :
      ( ( mult @ X3 @ three )
      = six ),
    file('/export/starexec/sandbox/tmp/tmp.tM0Tfutswe/E---3.1_25089.p',thm) ).

thf(six_ax,axiom,
    ( six
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.tM0Tfutswe/E---3.1_25089.p',six_ax) ).

thf(three_ax,axiom,
    ( three
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.tM0Tfutswe/E---3.1_25089.p',three_ax) ).

thf(mult_ax,axiom,
    ( mult
    = ( ^ [X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X1: $i > $i,X2: $i] : ( X4 @ ( X3 @ X1 ) @ X2 ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.tM0Tfutswe/E---3.1_25089.p',mult_ax) ).

thf(two_ax,axiom,
    ( two
    = ( ^ [X1: $i > $i,X2: $i] : ( X1 @ ( X1 @ X2 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.tM0Tfutswe/E---3.1_25089.p',two_ax) ).

thf(c_0_5,negated_conjecture,
    ~ ? [X3: ( $i > $i ) > $i > $i] :
        ( ( mult @ X3 @ three )
        = six ),
    inference(assume_negation,[status(cth)],[thm]) ).

thf(c_0_6,plain,
    ! [X18: $i > $i,X19: $i] :
      ( ( six @ X18 @ X19 )
      = ( X18 @ ( X18 @ ( X18 @ ( X18 @ ( X18 @ ( X18 @ X19 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[six_ax])]) ).

thf(c_0_7,plain,
    ! [X12: $i > $i,X13: $i] :
      ( ( three @ X12 @ X13 )
      = ( X12 @ ( X12 @ ( X12 @ X13 ) ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[three_ax])]) ).

thf(c_0_8,negated_conjecture,
    ! [X72: ( $i > $i ) > $i > $i] :
      ( ( mult @ X72 @ three )
     != six ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

thf(c_0_9,plain,
    ! [X35: ( $i > $i ) > $i > $i,X36: ( $i > $i ) > $i > $i,X37: $i > $i,X38: $i] :
      ( ( mult @ X35 @ X36 @ X37 @ X38 )
      = ( X35 @ ( X36 @ X37 ) @ X38 ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[mult_ax])]) ).

thf(c_0_10,plain,
    ! [X51: $i > $i,X52: $i] :
      ( ( six @ X51 @ X52 )
      = ( X51 @ ( X51 @ ( X51 @ ( X51 @ ( X51 @ ( X51 @ X52 ) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_6]) ).

thf(c_0_11,plain,
    ! [X45: $i > $i,X46: $i] :
      ( ( three @ X45 @ X46 )
      = ( X45 @ ( X45 @ ( X45 @ X46 ) ) ) ),
    inference(variable_rename,[status(thm)],[c_0_7]) ).

thf(c_0_12,plain,
    ! [X10: $i > $i,X11: $i] :
      ( ( two @ X10 @ X11 )
      = ( X10 @ ( X10 @ X11 ) ) ),
    inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[two_ax])]) ).

thf(c_0_13,negated_conjecture,
    ! [X3: ( $i > $i ) > $i > $i] :
      ( ( mult @ X3 @ three )
     != six ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

thf(c_0_14,plain,
    ! [X68: ( $i > $i ) > $i > $i,X69: ( $i > $i ) > $i > $i,X70: $i > $i,X71: $i] :
      ( ( mult @ X68 @ X69 @ X70 @ X71 )
      = ( X68 @ ( X69 @ X70 ) @ X71 ) ),
    inference(variable_rename,[status(thm)],[c_0_9]) ).

thf(c_0_15,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( six @ X1 @ X2 )
      = ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

thf(c_0_16,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( three @ X1 @ X2 )
      = ( X1 @ ( X1 @ ( X1 @ X2 ) ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

thf(c_0_17,plain,
    ! [X43: $i > $i,X44: $i] :
      ( ( two @ X43 @ X44 )
      = ( X43 @ ( X43 @ X44 ) ) ),
    inference(variable_rename,[status(thm)],[c_0_12]) ).

thf(c_0_18,negated_conjecture,
    ! [X3: ( $i > $i ) > $i > $i] :
      ( ( mult @ X3 @ three @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) )
     != ( six @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) ) ),
    inference(neg_ext,[status(thm)],[c_0_13]) ).

thf(c_0_19,plain,
    ! [X1: $i > $i,X4: ( $i > $i ) > $i > $i,X3: ( $i > $i ) > $i > $i,X2: $i] :
      ( ( mult @ X3 @ X4 @ X1 @ X2 )
      = ( X3 @ ( X4 @ X1 ) @ X2 ) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

thf(c_0_20,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( three @ X1 @ ( three @ X1 @ X2 ) )
      = ( six @ X1 @ X2 ) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).

thf(c_0_21,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( two @ X1 @ X2 )
      = ( X1 @ ( X1 @ X2 ) ) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

thf(c_0_22,negated_conjecture,
    ! [X3: ( $i > $i ) > $i > $i] :
      ( ( X3 @ ( three @ ( esk1_2 @ X3 ) ) @ ( esk2_1 @ X3 ) )
     != ( six @ ( esk1_2 @ X3 ) @ ( esk2_1 @ X3 ) ) ),
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

thf(c_0_23,plain,
    ! [X1: $i > $i,X2: $i] :
      ( ( two @ ( three @ X1 ) @ X2 )
      = ( six @ X1 @ X2 ) ),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

thf(c_0_24,negated_conjecture,
    $false,
    inference(spm,[status(thm)],[c_0_22,c_0_23]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : NUM020^1 : TPTP v8.1.2. Released v3.6.0.
% 0.04/0.14  % Command    : run_E %s %d THM
% 0.16/0.36  % Computer : n007.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri May  3 09:05:50 EDT 2024
% 0.16/0.36  % CPUTime    : 
% 0.22/0.50  Running higher-order theorem proving
% 0.22/0.50  Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.tM0Tfutswe/E---3.1_25089.p
% 0.22/0.52  # Version: 3.1.0-ho
% 0.22/0.52  # Preprocessing class: HSSSSMSSMSSNHHN.
% 0.22/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.52  # Starting pre_casc_2 with 1500s (5) cores
% 0.22/0.52  # Starting sh2 with 300s (1) cores
% 0.22/0.52  # Starting sh3 with 300s (1) cores
% 0.22/0.52  # Starting new_ho_10 with 300s (1) cores
% 0.22/0.52  # pre_casc_2 with pid 25218 completed with status 0
% 0.22/0.52  # Result found by pre_casc_2
% 0.22/0.52  # Preprocessing class: HSSSSMSSMSSNHHN.
% 0.22/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.52  # Starting pre_casc_2 with 1500s (5) cores
% 0.22/0.52  # No SInE strategy applied
% 0.22/0.52  # Search class: HUUPM-FFSF32-DHHSFMNN
% 0.22/0.52  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.52  # Starting pre_casc_2 with 901s (1) cores
% 0.22/0.52  # Starting sh2 with 151s (1) cores
% 0.22/0.52  # Starting sh3 with 151s (1) cores
% 0.22/0.52  # Starting sh9 with 151s (1) cores
% 0.22/0.52  # Starting new_ho_10 with 146s (1) cores
% 0.22/0.52  # new_ho_10 with pid 25232 completed with status 0
% 0.22/0.52  # Result found by new_ho_10
% 0.22/0.52  # Preprocessing class: HSSSSMSSMSSNHHN.
% 0.22/0.52  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.52  # Starting pre_casc_2 with 1500s (5) cores
% 0.22/0.52  # No SInE strategy applied
% 0.22/0.52  # Search class: HUUPM-FFSF32-DHHSFMNN
% 0.22/0.52  # Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.22/0.52  # Starting pre_casc_2 with 901s (1) cores
% 0.22/0.52  # Starting sh2 with 151s (1) cores
% 0.22/0.52  # Starting sh3 with 151s (1) cores
% 0.22/0.52  # Starting sh9 with 151s (1) cores
% 0.22/0.52  # Starting new_ho_10 with 146s (1) cores
% 0.22/0.52  # Preprocessing time       : 0.001 s
% 0.22/0.52  # Presaturation interreduction done
% 0.22/0.52  
% 0.22/0.52  # Proof found!
% 0.22/0.52  # SZS status Theorem
% 0.22/0.52  # SZS output start CNFRefutation
% See solution above
% 0.22/0.52  # Parsed axioms                        : 29
% 0.22/0.52  # Removed by relevancy pruning/SinE    : 0
% 0.22/0.52  # Initial clauses                      : 29
% 0.22/0.52  # Removed in clause preprocessing      : 14
% 0.22/0.52  # Initial clauses in saturation        : 15
% 0.22/0.52  # Processed clauses                    : 52
% 0.22/0.52  # ...of these trivial                  : 3
% 0.22/0.52  # ...subsumed                          : 0
% 0.22/0.52  # ...remaining for further processing  : 49
% 0.22/0.52  # Other redundant clauses eliminated   : 0
% 0.22/0.52  # Clauses deleted for lack of memory   : 0
% 0.22/0.52  # Backward-subsumed                    : 0
% 0.22/0.52  # Backward-rewritten                   : 3
% 0.22/0.52  # Generated clauses                    : 441
% 0.22/0.52  # ...of the previous two non-redundant : 435
% 0.22/0.52  # ...aggressively subsumed             : 0
% 0.22/0.52  # Contextual simplify-reflections      : 0
% 0.22/0.52  # Paramodulations                      : 431
% 0.22/0.52  # Factorizations                       : 0
% 0.22/0.52  # NegExts                              : 5
% 0.22/0.52  # Equation resolutions                 : 0
% 0.22/0.52  # Disequality decompositions           : 0
% 0.22/0.52  # Total rewrite steps                  : 193
% 0.22/0.52  # ...of those cached                   : 146
% 0.22/0.52  # Propositional unsat checks           : 0
% 0.22/0.52  #    Propositional check models        : 0
% 0.22/0.52  #    Propositional check unsatisfiable : 0
% 0.22/0.52  #    Propositional clauses             : 0
% 0.22/0.52  #    Propositional clauses after purity: 0
% 0.22/0.52  #    Propositional unsat core size     : 0
% 0.22/0.52  #    Propositional preprocessing time  : 0.000
% 0.22/0.52  #    Propositional encoding time       : 0.000
% 0.22/0.52  #    Propositional solver time         : 0.000
% 0.22/0.52  #    Success case prop preproc time    : 0.000
% 0.22/0.52  #    Success case prop encoding time   : 0.000
% 0.22/0.52  #    Success case prop solver time     : 0.000
% 0.22/0.52  # Current number of processed clauses  : 31
% 0.22/0.52  #    Positive orientable unit clauses  : 11
% 0.22/0.52  #    Positive unorientable unit clauses: 9
% 0.22/0.52  #    Negative unit clauses             : 11
% 0.22/0.52  #    Non-unit-clauses                  : 0
% 0.22/0.52  # Current number of unprocessed clauses: 396
% 0.22/0.52  # ...number of literals in the above   : 396
% 0.22/0.52  # Current number of archived formulas  : 0
% 0.22/0.52  # Current number of archived clauses   : 18
% 0.22/0.52  # Clause-clause subsumption calls (NU) : 0
% 0.22/0.52  # Rec. Clause-clause subsumption calls : 0
% 0.22/0.52  # Non-unit clause-clause subsumptions  : 0
% 0.22/0.52  # Unit Clause-clause subsumption calls : 64
% 0.22/0.52  # Rewrite failures with RHS unbound    : 0
% 0.22/0.52  # BW rewrite match attempts            : 512
% 0.22/0.52  # BW rewrite match successes           : 12
% 0.22/0.52  # Condensation attempts                : 52
% 0.22/0.52  # Condensation successes               : 0
% 0.22/0.52  # Termbank termtop insertions          : 7770
% 0.22/0.52  # Search garbage collected termcells   : 87
% 0.22/0.52  
% 0.22/0.52  # -------------------------------------------------
% 0.22/0.52  # User time                : 0.012 s
% 0.22/0.52  # System time              : 0.004 s
% 0.22/0.52  # Total time               : 0.016 s
% 0.22/0.52  # Maximum resident set size: 1832 pages
% 0.22/0.52  
% 0.22/0.52  # -------------------------------------------------
% 0.22/0.52  # User time                : 0.064 s
% 0.22/0.52  # System time              : 0.011 s
% 0.22/0.52  # Total time               : 0.075 s
% 0.22/0.52  # Maximum resident set size: 1744 pages
% 0.22/0.52  % E---3.1 exiting
% 0.22/0.53  % E exiting
%------------------------------------------------------------------------------